A triangularity result for associated varieties of highest weight modules

We prove a conjecture of Tanisaki in the classical case, which says roughly that the matrix of orbital varieties occurring in the associated variety of a simple highest weight module is upper triangular.     

Quantitative imaging of 33P in plant materials using 14C polymer references

Analytical and Bioanalytical Chemistry - Phosphorus (P) research still lacks techniques for rapid imaging of P use and allocation in different soil, sediment, and biological systems in a...     

Fast image method for impulse response calculations of box-shaped rooms

The image method has been used for calculating the impulse response of box-shaped rooms for over 25 years. While this method is functional, it can be inefficient because many of the commonly used mathematical operations are either redundant or unnecessary. This paper addresses these two inefficiencies by proposing both the use of look-up tables to prevent redundant calculations, and the use of a sorting method to allow the prevention of unnecessary calculations. Either technique, by itself, results in a large reduction in computation time. The greatest time reductions, however, can be achieved when both techniques are used together.     

Pulsed quantum cascade laser instrument with compact design for rapid, high sensitivity measurements of trace gases in air

We have developed a compact instrument for sensitive, rapid and continuous measurement of trace gases in air, with results presented here for methane (CH₄), nitric oxide (NO), nitrous oxide (N₂O) and ammonia (NH₃). This instrument takes advantage of recent technology in quantum cascade (QC) lasers and infrared detectors, which allows high sensitivity without cryogenic liquids, e.g., 0.2 ppb (0.2×10^-9) of NH₃ in air in 1 s. One may substitute a QC laser operating at a different wavelength to measure other gases. The instrument operates continuously, requiring little operator attention, and web-based remote access is provided for instrument control, calibration and data retrieval. The instrument design includes a thermoelectrically (TE) cooled pulsed distributed feedback (DFB) QC laser, a low volume (0.5 l) multipass cell offering 76 m absorption path length and a TE cooled detector. Integrated software for laser control and data analysis using direct absorption provides quantitative trace gas measurements without calibration gases. The instrument may be applied to field measurements of gases of environmental concern. PACS  07.57.Ty; 42.62.Fi; 92.70.Cp     

Weakly least integer closed groups

An archimedean lattice-ordered groupA with distinguished weak unit has the canonical Yosida representation as an ℓ-group of extended real-valued functions on a certain compact Hausdorff spaceY A. Such an ℓ-groupA is calledleast integer closed, orLIC (resp.,weakly least integer closed, orwLIC) if, in the representation,a ∈A implies [a] ∈A (resp., there isa′ ∈A witha′=[a] on a dense set inY A), where [r] ≡ the least integer greater than or equal tor. Earlier, we have studiedLIC groups, with an emphasis on their a-extensions. Here, we turn towLIC groups: we give an intrinsic (though awk-ward) characterization in terms of existence of certain countable suprema. This results also in an intrinsic characterization ofLIC, previously lacking. Also,wLIC is a hull class (whichLIC is not), and the hullwlA is “somewhere near” the projectable hullpA. The best comparison comes from a (somewhat novel) factoringpA=loc(wpA), wherewpA is the “weakly projectable” hull (defined here), andlocB is the “local monoreflection”; then,wpA≤wlA≤loc(wpA), andpA≤loc(wlA), while with a strong unit, all these coincide. Numerous examples and special cases are examined.     

Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory

We calculate the amplitude T₁ for forward doubly virtual Compton scattering in heavy-baryon chiral perturbation theory, to fourth order in the chiral expansion and with the leading contribution of the $ \gamma$ N $ \Delta$ form factor. This provides a model-independent expression for the amplitude in the low-momentum region, which is the dominant one for its contribution to the Lamb shift. It allows us to significantly reduce the theoretical uncertainty in the proton polarisability contributions to the Lamb shift in muonic hydrogen. We also stress the importance of consistency between the definitions of the Born and structure parts of the amplitude. Our result leaves no room for any effect large enough to explain the discrepancy between proton charge radii as determined from muonic and normal hydrogen.     

Local structure of OH adsorbed on the Ge(0 0 1)(2 × 1) surface using scanned-energy mode photoelectron diffraction

The local geometry of OH fragments adsorbed on the Ge(0 0 1)(2 × 1) surface has been examined using O 1s scanned energy mode photoelectron diffraction. These fragments were obtained by the dissociative reaction of the clean surface with H₂O. The Ge–O bond length is found to be 1.76 ± 0.02 Å and the Ge–O bond angle to be 15° ± 2° relative to the surface normal. Some information about the positions of the Ge dimer atoms has also been obtained.     

Neat rings

A ring is called clean if every element is the sum of a unit and an idempotent. Throughout the last 30 years several characterizations of commutative clean rings have been given. We have compiled a thorough list, including some new equivalences, in hopes that in the future there will be a better understanding of this interesting class of rings. One of the fundamental properties of clean rings is that every homomorphic image of a clean ring is clean. We define a neat ring to be one for which every proper homomorphic image is clean. In particular, the ring of integers, Z, and any nonlocal PID are examples neat rings which are not clean. We characterize neat Bézout domains using the group of divisibility. In particular, it is shown that a neat Bézout domain has stranded primes, that is, for every nonzero prime ideal the set of primes either containing or contained in the given prime forms a chain under set-theoretic inclusion.     

Feebly Projectable Algebraic Frames and Multiplicative Filters of Ideals

In the article (Martinez and Zenk, Algebra Universalis, 50, 231–257, 2003.), the authors studied several conditions on an algebraic frame L. In particular, four properties called Reg(1), Reg(2), Reg(3), and Reg(4) were considered. There it was shown that Reg(3) is equivalent to the more familiar condition known as projectability. In this article we show that there is a nice property, which we call feebly projectable, that is between Reg(3) and Reg(4). In the main section of the article we apply our notions to the frame of multiplicative filters of ideals in a commutative ring with unit and give characterizations of several well-known classes of commutative rings.